We derive analytical formulas quantifying radiative emission from
subwavelength emitters embedded in triply resonant nonlinear χ(2)
cavities supporting exceptional points (EP) made of dark and leaky modes. We
show that the up-converted radiation rate in such a system can be greatly
enhanced---by up to two orders of magnitude---compared to typical Purcell
factors achievable in non-degenerate cavities, for both monochromatic and
broadband emitters. We provide a proof-of-concept demonstration by studying an
inverse-designed 2D photonic-crystal slab that supports an EP formed out of a
Dirac cone at the emission frequency and a phase-matched, leaky-mode resonance
at the second harmonic frequency
